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8.32 (1982)

Solved

Suppose $G$ is a finitely generated group such that, for any set $\pi$ of primes and any subgroup $H$ of $G$, if $G/\langle H^G \rangle$ is a finite $\pi$-group then $|G : H|$ is a finite $\pi$-number. Is $G$ nilpotent? This is true for finitely generated soluble groups.

Contributor: J. C. Lennox

Progress

Not always (V. N. Obraztsov, J. Austral. Math. Soc. (A), 61, no. 2 (1996), 267–288).

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